Territory membership versus role hierarchy access
Key Takeaway
Access that users get through territories to accounts, opportunities, contacts, and cases rolls up to the role hierarchy. Users in higher roles already have that access without being assigned to a territory.
Salesforce has two separate hierarchies that open record access upward to users who don't own the records. The role hierarchy gives managers access to records owned by or shared with users below them. Territories give users access to accounts and related records based on the territories they're assigned to. To predict who can see what, work out which hierarchy drives a user's access and how the Grant Access Using Hierarchies setting affects both.
Role hierarchy access
The role hierarchy opens access vertically. Users in higher roles get access to records owned by or shared with users in roles below them. You don't need sharing rules for this access.
Your org's role hierarchy puts a Support Manager role above a Support Agent role. Support Managers automatically get access to every record that Support Agents own. They also get access to every record that Support Agents get through sharing rules, manual sharing, or other features. Nobody has to create a sharing rule to make this happen.
The role hierarchy fits management and HR structures where each person reports to only one other person.